# General method for cases involving buckling (6.3.4)

If the above assessments can not apply, for example due to

• non uniform members,
• complex support conditions,

then this general method is used.

$$$$\frac{\chi_{op} \cdot \alpha_{alt,k}}{\gamma_{M1}} \geq 1.0,$$$$
$\chi_{op} = \min\{\chi, \chi_{LT}\}$

Reduction factor expressing effect of buckling $\chi_{op} = \min\{\chi, \chi_{LT}\}$. Parameters $\chi, \chi_{LT}$ are again functions of $\{\overline{\lambda}, \dots\}$, in this case $\chi,\chi_{LT} = f(\overline{\lambda}_{op},\dots)$, where

$$$$\overline{\lambda}_{op} = \sqrt{\frac{\alpha_{ult,k}}{\alpha_{cr,op}}}$$$$
• Factor $\alpha_{ult,k}$ is the mimimum amplifier of design load such, that characteristic resistance (yield or ultimate according to configuration) is reached while buckling is ignored.
• Factor $\alpha_{cr,op}$ is the minimum amplifier of the same design load such, that critical elastic resistance is reached with regards to buckling.

Both $\alpha_{cr,op}$ and $\alpha_{ult,k}$ might be determined from FEM (finite element method) analysis.

Example: if the assessment of a member is evaluated as

$$\frac{N_{Ed}}{N_{Rk}} + \frac{M_{Ed}}{M_{y,Rk}} \leq 1$$

then the minimum amplifier for the load to reach resistance is obtained from

$$\alpha_{ult,k} \left( \frac{N_{Ed}}{N_{Rk}} + \frac{M_{Ed}}{M_{y,Rk}} \right) = 1 \hskip2em \implies \hskip2em \alpha_{ult,k}$$

and the assessment is

$$\frac{N_{Ed}}{N_{Rk}/\gamma_{M1}} + \frac{M_{Ed}}{M_{y,Rk}/\gamma_{M1}} \leq 1 \cdot \chi_{op}$$

List of chapters